I just got a tiny little bunny. What do they eat? what's good and what's bad?

Excellent diet guidance, including links to lists of appropriate vegetables can be found here: http://www.rabbit.org/faq/sections/diet.html The most important part of a rabbit's diet is unlimited high quality hay. A good quality pellet should be offered (unlimited until around 6-7 months, then limited in quantity), and vegetables should be introduced slowly beginning at 12 weeks of age.

You will get more and better responses posting in the 'other pets' section- rabbits are not rodents, they are lagomorphs.

Add: Iceburg lettuce is the one to avoid, as it can give them diarrhea. Most other greens are fine, start with just one type, adding in new vegetables slowly, and watching for stomach upset. Spinach is safe, as are dark-colored leaf lettuces and most all cooking greens. The list at the website I posted will give you more ideas for safe vegetables. The dietary guidance there is vet formulated and approved. My current board-certified exotics veterinarian recommends the same feeding program that is outlined there, as have the last three vets I used at previous locations.

You don't give them lettuce because it's basically all water, it does nothing for them. If given too much it will cause your bunny to get the runs. I fed my rabbits 8 in 1 Ecotrition Organic Blend for Rabbits.

My bunny always use to enjoy:

Bok Choi

Corn

Carrots

hot toast with a tiny spread of jam

Pellets

and once a month i use to give her a tiny teddy

for food I'd go with whatever standard rabbit chow you get from your local pet store.

as far as other things or if you want to give it a treat, I've had several rabbits of multiple breeds and a guinea pig, and all of them have gone nuts over spinach.